Sampling the Grand Canonical Ensemble with Multisite λ Dynamics

Molecular simulation in the grand canonical ensemble is widely used to study a diverse range of systems and processes, such as water networks in biological macromolecules, drug binding, and the adsorption of molecules at an interface. Here, we develop grand canonical multisite lambda dynamics (GC-MSλD) to sample fluctuations in molecule number by coupling the molecules of interest to a dynamic λ variable. The chemical potential, set as a λ-dependent energetic bias, is used to control the number of molecules. We anticipate that GC-MSλD may equilibrate faster and with less computational overhead than some GCMC/MD algorithms. We demonstrate the use of the GC-MSλD framework to control the number of molecules in a box of TIP3P water. Next, we apply the methodology to sample crystallographic water occupancies in a protein cavity and to compute protein-ligand binding free energies involving water displacement.